Or will the movies attempt to go on without him?
There are little grace notes of fun to be found in the movie: Bardem's cheesy over-enunciation of "Jack Sparrow" is delightful; Geoffrey Rush still wrestling some poignancy from his Captain Barbossa character; the original theme from composer Hans Zimmer can probably still shiver your timbers after all these years. (I'm saddened to report that Paul McCartney's cameo is so brief and inconsequential it barely registers.) Again, most of these pleasures are independent of Depp, suggesting the series could benefit from a total reboot or pivot.
Here's one thing in the movie that doesn't work: the reappearance of Orlando Bloom and Keira Knightley as Will and Elizabeth Turner, the parents of this film's bland pseudo-protagonist Henry Turner (Brenton Thwaites). Bloom appears in the prologue at the beginning of the movie, living a cursed life aboard the Flying Dutchman, and he appears again at its close once his curse has been lifted. In a bizarre moment at the end, Knightley's Elizabeth appears seemingly from nowhere over a hill, runs into Will's arms, and kisses him for a mushy reunion. (In a fitting twist for this dude-centric film, Knightley has zero lines.)
It's a scene that speaks to the awkward way Pirates, a product of the pre-Marvel era, has struggled to fit into the fan-service-ey demands of modern blockbuster-dom. Unless you are a diehard Pirates fan, you probably don't even remember what happened to Will or Elizabeth in the previous movies. Similarly, when the tentacle-faced villain Davy Jones (Bill Nighy) appears in the perfunctory post-credits scene, waking Will from a good night's sleep, you'll struggle to remember why he's important. The truth is he's not.
These post-credits scene are just chum tossed in the internet waters. As Bustle points out, the last film in the Pirates series, 2011's Bloom-and-Knightley-less On Stranger Tides, ended with a tag of Penelope Cruz's character Angelica discovering a Jack Sparrow voodoo doll. That scene had no bearing on this new film. Compared to the dutiful storytelling of Marvel, there's something almost charming about the haphazard way these Pirates movies treat the larger narrative world of the series. When nothing matters, anything can happen.
This may not be a "Dark Universe" movie... but maybe it could be? What if Jack Sparrow is actually The Mummy? What if Bardem's character is secretly Frankenstein? What if the monkey is... the Wolfman? Dead men may tell no tales, but they sure do print money.